CN109257148B - Polarization code BP decoding method based on Gaussian approximate threshold judgment - Google Patents

Polarization code BP decoding method based on Gaussian approximate threshold judgment Download PDF

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CN109257148B
CN109257148B CN201811417331.XA CN201811417331A CN109257148B CN 109257148 B CN109257148 B CN 109257148B CN 201811417331 A CN201811417331 A CN 201811417331A CN 109257148 B CN109257148 B CN 109257148B
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CN109257148A (en
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费泽松
王璐
孙策
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Beijing Institute of Technology BIT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1105—Decoding
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2948—Iterative decoding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0047—Decoding adapted to other signal detection operation
    • H04L1/005—Iterative decoding, including iteration between signal detection and decoding operation
    • H04L1/0051—Stopping criteria
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
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    • H04L1/0056—Systems characterized by the type of code used
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Abstract

The invention relates to a polarization code BP decoding method based on Gaussian approximate threshold judgment, and belongs to the technical field of channel coding and decoding. The CRC check module is added in the transmission process, and the information value judgment threshold is set for each bit node at the receiving end according to the principle of Gaussian approximation. In the process of each iteration, the information value of each bit node is compared with the corresponding judgment threshold value, the bit nodes exceeding the threshold value are gradually screened out and the updating is stopped, and the information values of the bit nodes not exceeding the threshold value are continuously updated. And after each iteration is finished, judging the decoding result, performing CRC (cyclic redundancy check) check, stopping the iteration if the decoding result passes the check, and otherwise, continuing the iteration until the maximum iteration number is reached. The invention reduces the calculation complexity of decoding and saves the calculation resources on the basis of ensuring the decoding performance.

Description

Polarization code BP decoding method based on Gaussian approximate threshold judgment
Technical Field
The invention relates to a polarization code BP decoding method based on Gaussian approximate threshold judgment, and belongs to the technical field of channel coding and decoding.
Background
The fifth generation mobile communication system (5G) is developed to meet the demand for a drastic increase in data traffic and the number of device connections, ultra-low latency, and the like. To meet these index requirements, 5G must be technically broken through in various aspects. Because of interference and fading in the wireless channel, the signal may be corrupted during transmission, and the channel coding technique resists and corrects errors caused by a bad channel by increasing the amount of information redundancy. The efficient coding and decoding scheme can reduce the service overhead of the system, increase the coverage rate of the network and the reliability of data transmission, and improve the spectrum efficiency. The channel coding algorithm which can reach or approach the system channel capacity is constructed, the complexity of the decoding algorithm is reduced, and the method is always a research target in the channel coding and decoding technology.
The development of channel coding goes from convolutional codes of 2G systems to Turbo codes of 3G and 4G systems, and the continuously evolving and developing channel coding technology provides effective guarantee for efficient and reliable communication links. Since 5G has a high requirement for performance index, the previous channel coding techniques can no longer meet the requirement. The international radio standardization organization (3 GPP) determines that a channel coding scheme of a 5G traffic channel is a low-density parity-check (LDPC) code, and a channel coding scheme of a control channel is a polar code. The polarization code is firstly proposed by Erdal arika in 2007, is the only encoding mode which can be theoretically proved to reach the shannon limit at present, and the encoding and decoding capability of the linear complexity is very practical.
The coding of the polarization code is based on the channel polarization phenomenon, independent channels with the same property are combined into one channel, and then the channel is split into mutually independent polarization channels according to the transition probability, so that the capacity of each channel is in a polarization distribution state. And information bits are transmitted on the polarized channel with higher capacity, and frozen bits known by both transmitting and receiving are transmitted on the polarized channel with lower capacity.
For the decoding algorithm of the polar code, arika in its article provides a recursive structure-based Serial Cancellation (SC) decoding algorithm, which has low decoding complexity, but the decoding of the transmission bits of each channel is related to each other, which may cause error transmission. In subsequent researches, improvements to the SC algorithm appear, including a serial elimination List (SCL) decoding algorithm and a CRC-assisted serial elimination List (CA-SCL) decoding algorithm, which all improve performance.
The SC decoding algorithm and the improved decoding algorithm thereof have better performance and lower decoding complexity, but have higher decoding time delay. Based on the research on the polar code decoding, a Belief Propagation (BP) algorithm appears, the decoding delay is very low due to a parallel decoding structure, the calculation complexity of the decoding process is high due to a large number of iteration times, and the realization difficulty is high.
Disclosure of Invention
The invention aims to provide a polarization code BP decoding method based on Gaussian approximate threshold judgment aiming at the technical defect of high complexity of the existing polarization code BP decoding algorithm, and the calculation complexity of BP decoding is reduced on the premise of ensuring decoding performance.
The core idea of the invention is as follows: adding CRC check bits in the encoding process, setting a threshold value of the information value of each bit node based on Gaussian approximation by a decoding end, comparing the information value of each bit node with the threshold value in the process of each iteration, stopping updating the information value if the information value exceeds the threshold value, and otherwise, continuing to update; and performing CRC (cyclic redundancy check) on the decoding judgment result after each iteration, if the decoding judgment result passes the CRC, terminating the iteration in advance, and otherwise, continuing the iteration until the maximum iteration number is reached.
The information value is a Log Likelihood Ratio, is called Log Likelihood Ratio in English and is abbreviated as LLR;
defining the sequence of information bits at the sender as u0,u1,...,uK-1(ii) a The sequence obtained by adding the CRC check code is u0′,u1′,...,uK′-1'; for u is paired0′,u1′,...,uK′-1' the sequence obtained after polar coding is x0,x1,...,xN-1(ii) a The sequence obtained by the demodulation of the receiving end is y0,y1,...,yN-1(ii) a There are two types of information in the decoding process, information passing from left to right, namely right information Ri,j(ii) a Information passing from right to left, i.e. left information Li,j(ii) a LetterThe threshold value for determining the information value is Ti,j(ii) a The maximum number of decoding iterations is Iter;
a polarization code BP decoding method based on Gaussian approximate threshold judgment specifically comprises the following steps:
step one, a sending end pair information bit sequence u0,u1,...,uK-1Performing CRC to obtain a sequence u0′,u1′,...,uK′-1', realigning the sequence u0′,u1′,...,uK′-1' polar coding to obtain polar coded sequence, denoted as x0,x1,...,xN-1；
Wherein, the CRC check code adopts a 24-bit check code;
polar coding is based on X ═ U' G; x ═ X0,x1,...,xN-1；U'＝u0′,u1′,...,uK′-1', G is a generation matrix;
step two, BP decoding is based on the sequence y obtained by demodulating the receiving end by the factor graph0,y1,...,yN-1Performing decoding initialization, specifically including the following substeps:
step 2.A sets the information value of the leftmost bit node as
Figure GDA0002414309080000021
And is initialized to formula (1);
Figure GDA0002414309080000022
wherein, R represents the information which is transmitted from left to right in the two types of information existing in the decoding process, namely the right information;
Figure GDA0002414309080000023
the superscript 0 of the subscript denotes the 0 th iteration, the 0 on the left of the subscript denotes the 0 th state in the factor graph, and the j on the right denotes the j th bit node in the factor graph; a represents a set of information bits; a. theCRepresents a set of frozen bits;
step 2.B will right side bit node signalInformation value is set as
Figure GDA0002414309080000031
Representing the message transmitted by the channel, and initializing to the formula (2);
Figure GDA0002414309080000032
wherein, L represents the information which is transmitted from right to left in the two types of information in the decoding process, namely left information;
Figure GDA0002414309080000033
the upper label 0 in the index represents the 0 th iteration, the S on the left of the index represents the S state in the factor graph, and the j on the right represents the j bit node in the factor graph; ln is the logarithm of the base e; p (y)j|xj0) represents the jth bit node y at the receiving endjProbability of correctly judging as 0; p (y)j|xj1) denotes the jth bit node y at the receiving endjProbability of correctly judging as 1;
step 2.C, initializing the information values of the rest bit nodes in the factor graph to 0;
step three, setting a judgment threshold T of an information value for each bit nodei,jAnd a maximum number of iterations Iter;
wherein the threshold value T is determinedi,jThe setting of (2) is based on a Gaussian approximation algorithm, and specifically comprises the following sub-steps:
step 3, setting of a judgment threshold value of a bit node connected with an additive check node in the A factor graph is obtained based on the formula (3) recursion;
Figure DEST_PATH_BDA0001879790350000034
wherein, the number on the left side of the subscript represents the number of states in the factor graph, i represents the ith state, and i +1 represents the (i + 1) th state; the numbers to the right of the subscript indicate the number of bit nodes in the factor graph, i.e., j indicates the jth bit node, j +2iDenotes the j +2 thiA bit node;
the initial threshold value for iteration is the initialization information value set in the step two;
Figure GDA0002414309080000035
the function is defined as formula (4);
Figure GDA0002414309080000036
step 3, setting the judgment threshold value of the bit node connected with the direct connection check node in the B factor graph is obtained by recursion based on the formula (5);
Figure GDA0002414309080000041
wherein, the number on the left side of the subscript represents the number of states in the factor graph, i represents the ith state, and i +1 represents the (i + 1) th state; the numbers to the right of the subscript indicate the number of bit nodes in the factor graph, i.e., j indicates the jth bit node, j +2iDenotes the j +2 thiA bit node;
step four, information values are transmitted to the left from the rightmost end bit node, and the method specifically comprises the following steps:
in the process of transmission, the information value of each current bit node is compared with a threshold value T set for each nodei,jComparing, if the threshold value is exceeded, transmitting the information value according to the formula (6), otherwise, updating leftwards according to the formula (7) and transmitting the information value of each bit node;
Figure GDA0002414309080000042
Figure GDA0002414309080000043
wherein i represents the ith state in the factor graph, j represents the jth bit node in the factor graph, t represents the tth iteration, and g (x, y) is 2tanh-1(tanh (x/2) tanh (y/2)), the calculation can be simplified to a minimum sum algorithmg(x,y)≈0.9sign(x)sign(y)min(|x|,|y|)；
Step five, transferring an information value from the leftmost bit node to the right, specifically:
the information value of each current bit node is compared with a threshold value T set for each nodei,jComparing, and if the comparison result exceeds the threshold value, transmitting the information value according to the formula (6); otherwise, updating and transmitting the information value of each bit node to the right according to the formula (8);
Figure GDA0002414309080000044
step six, information values are transmitted to the left from the rightmost end bit node, and the method specifically comprises the following steps:
the information value of each current bit node is compared with a threshold value T set for each nodei,jComparing, if the comparison result exceeds the threshold value, transmitting the information value according to the formula (6), otherwise, updating leftwards according to the formula (7) and transmitting the information value of each bit node;
the information value of each bit node is transmitted back and forth according to the fifth step and the sixth step, namely, the decoding process is that the information value of each bit node is continuously transmitted back and forth between adjacent states in the factor graph, namely, the process of the fifth step and the sixth step is continuously repeated;
step seven, the appointed information value is transmitted from the leftmost end to the rightmost end and then transmitted from the rightmost end to the leftmost end, and an iteration process is performed, namely, each time an iteration is completed, the iteration is performed once corresponding to the step five and the step six;
after each iteration process is finished, decoding judgment is carried out on each leftmost bit node according to the formula (9);
Figure GDA0002414309080000051
Figure GDA0002414309080000052
representing the decoding result of the jth bit node in the factor graph;
Figure GDA0002414309080000053
iter in (1) represents the maximum number of iterations;
step eight, judging whether the current iteration number reaches the maximum iteration number Iter, if so, jumping to the step ten, otherwise, jumping to the step nine;
step nine, performing CRC check on the decoding result, if the decoding result passes the CRC check, terminating the iteration process, and jumping to the step ten; otherwise, jumping to the step five, and continuing to perform the next iteration process;
step ten, outputting a decoding result;
therefore, through the steps from one to ten, the polarization code BP decoding method based on the Gaussian approximation threshold judgment is realized.
Advantageous effects
The invention provides a polarization code BP decoding method based on Gaussian approximate threshold judgment, which has the following beneficial effects compared with the prior art:
1. a CRC (cyclic redundancy check) module is added in the coding and decoding process, CRC check is carried out on the decoding judgment result after each iteration is finished, and the iteration can be terminated in advance through the check, so that the reliability of decoding is improved, the calculation resources are saved, and the decoding calculation complexity is reduced;
2. setting an information comparison threshold for each bit node according to the principle of a Gaussian approximation algorithm, and stopping iterative updating of the information value of the bit node if the information value of the current bit node is greater than the threshold; the threshold is set, so that the calculation complexity of the whole decoding process is reduced on the basis of ensuring the reliability of the decoding result.
Drawings
FIG. 1 is a factor graph example involved in the decoding process of the "polarization code BP decoding method based on Gaussian approximate threshold judgment" of the present invention;
FIG. 2 is an overall flowchart of "a method for decoding a polarization code BP based on Gaussian approximate threshold judgment" according to the present invention;
FIG. 3 is a graph showing a simulation relationship between BLER and SNR in an embodiment of the present invention, "a polarization code BP decoding method based on Gaussian approximation threshold determination";
fig. 4 shows the computational complexity of decoding in an embodiment of the present invention, "a polarization code BP decoding method based on gaussian approximation threshold determination".
Detailed Description
The invention is described in detail below with reference to the drawings and specific examples.
Example 1
In this embodiment, a CRC check code of 24 bits is added to an information sequence u with a length of 40 bits at a transmitting end, polar coding and QPSK modulation are performed, and the information sequence u is transmitted in an AWGN channel, where the code length is 128 bits. And decoding at a receiving end by adopting the polarization code BP decoding method based on the Gaussian approximate threshold judgment provided by the invention. And simulating a communication link to obtain a relation curve of SNR and BLER and the computational complexity saved by decoding. Meanwhile, the BLER obtained by simulation of the traditional polarization code BP decoding mode is compared under the same condition, and the effect of the method is verified. Fig. 1 is an example of a factor graph involved in the decoding process of the "polarization code BP decoding method based on gaussian approximation threshold determination" of the present invention, and the factor graph is exemplified by N-8 and K-3. FIG. 2 is an overall flowchart of "a method for decoding a polarization code BP based on Gaussian approximate threshold judgment" according to the present invention; FIG. 3 is a graph showing a simulation relationship between BLER and SNR in an embodiment of the present invention, "a polarization code BP decoding method based on Gaussian approximation threshold determination"; fig. 4 shows the computational complexity of decoding in an embodiment of the present invention, "a polarization code BP decoding method based on gaussian approximation threshold determination".
The specific operation flow is as follows:
step A, for the information sequence u with the length of 40 bits0,u1,...,u39Performing CRC, adding 24-bit CRC code to obtain sequence u0′,u1′,...,u63′；
Step B, sequence u is aligned0′,u1′,...,u63' polar coding is carried out, the code length is 128 bits, and a coded sequence x is obtained0,x1,...,x127；
Step C, QPSK modulation is carried out on the coded sequence, and the coded sequence is transmitted in an AWGN channel;
step D, obtaining a sequence y after the receiving end demodulates0,y1,...,y127Sending the data to a decoder for decoding; firstly, initializing, namely initializing the information value of the leftmost bit node according to the formula (1)
Figure GDA0002414309080000061
Initializing information value of rightmost bit node according to formula (2)
Figure GDA0002414309080000062
Initializing the information values of the other bit nodes to 0;
step E, setting an information value judgment threshold T for each bit node according to the formulas (3), (4) and (5)i,jSetting the maximum iteration number Iter to be 10;
step F, transmitting information values from the right bit node to the left, and in the transmission process, the information values of the current bit nodes and the threshold value T set for the nodes are comparedi,jComparing, if the information value exceeds the threshold value, transmitting the information value according to the formula (6), or updating leftwards according to the formula (7) and transmitting the information value of each bit node;
g, transferring information values from the left end bit nodes to the right, and in the transferring process, comparing the information values of the current bit nodes with the threshold T set for the nodesi,jComparing, and if the comparison result exceeds the threshold value, transmitting the information value according to the formula (6); otherwise, updating and transmitting the information value of each bit node to the right according to the formula (8);
h, transmitting information values from the rightmost bit node to the left, and in the transmission process, comparing the information values of the current bit nodes with the threshold T set for the nodesi,jComparing, if the comparison result exceeds the threshold value, transmitting the information value according to the formula (6), otherwise, updating leftwards according to the formula (7) and transmitting the information value of each bit node;
step I, the information value of each bit node is transmitted back and forth according to the step G and the step H, namely, the decoding process is that the information value of each bit node is continuously transmitted back and forth between adjacent states in the factor graph, namely the process of the step G and the step H is continuously repeated;
the appointed information value is transmitted from the leftmost end to the rightmost end and then transmitted from the rightmost end to the leftmost end, namely, each time iteration is completed, the iteration is executed once corresponding to the step G and the step H;
after each iteration process is finished, decoding judgment is carried out on each leftmost bit node according to the formula (9);
step J, judging whether the current iteration number reaches the maximum iteration number of 10, if so, jumping to step L, otherwise, jumping to step K;
step K, performing CRC (cyclic redundancy check) on the decoding result, if the decoding result passes the CRC, terminating the iteration process, and jumping to the step L; otherwise, jumping to the step G, and continuing to perform the next iteration process;
and L, outputting a decoding result.
From step a to step L, the polar code BP decoding method based on the gaussian approximation threshold judgment of the present embodiment is completed.
The simulation results of embodiment 1 are shown in fig. 3 and 4, and fig. 3 shows the BLER of the polarization code BP decoding method (code length is 128 bits) based on the gaussian approximation threshold judgment and the BLER of the conventional polarization code BP decoding under the same simulation conditions. Fig. 4 shows the computational complexity saved by decoding the polarization code BP decoding method (the code length is 128 bits) based on the gaussian approximation threshold judgment.
As can be seen from fig. 3, the performance of the polar code BP decoding method judged based on the gaussian approximation threshold is very close to that of the conventional polar code BP decoding method; as can be seen from fig. 4, the polarization code BP decoding method based on the gaussian approximation threshold judgment saves the calculation complexity compared with the conventional polarization code BP decoding method. Therefore, the polarization code BP decoding method based on the Gaussian approximate threshold judgment can reduce the calculation complexity of decoding on the basis of ensuring the decoding performance.
While the foregoing is directed to the preferred embodiment of the present invention, it is not intended that the invention be limited to the embodiment and the drawings disclosed herein. Equivalents and modifications may be made without departing from the spirit of the disclosure, which is to be considered as within the scope of the invention.

Claims (4)

1. A polarization code BP decoding method based on Gaussian approximate threshold judgment is characterized in that: the method comprises the following steps:
step one, a sending end pair information bit sequence u0,u1,...,uK-1Performing CRC to obtain a sequence u0′,u1′,...,uK′-1', realigning the sequence u0′,u1′,...,uK′-1' polar coding to obtain polar coded sequence, denoted as x0,x1,...,xN-1；
polar coding is based on X ═ U' G; x ═ X0,x1,...,xN-1；U'＝u0′,u1′,...,uK′-1', G is a generation matrix;
step two, BP decoding is based on the sequence y obtained by demodulating the receiving end by the factor graph0,y1,...,yN-1Performing decoding initialization, specifically including the following substeps:
step 2.A sets the information value of the leftmost bit node as
Figure FDA0002414309070000011
And is initialized to formula (1);
Figure FDA0002414309070000012
the information value is a Log Likelihood Ratio, is called Log Likelihood Ratio in English and is abbreviated as LLR;
wherein, R represents the information which is transmitted from left to right in the two types of information existing in the decoding process, namely the right information;
Figure FDA0002414309070000013
the superscript 0 of the subscript denotes the 0 th iteration, the 0 on the left of the subscript denotes the 0 th state in the factor graph, and the j on the right denotes the j th bit node in the factor graph; a represents a set of information bits; a. theCRepresents a set of frozen bits;
step 2.B sets the information value of the rightmost bit node as
Figure FDA0002414309070000014
Representing the message transmitted by the channel, and initializing to the formula (2);
Figure FDA0002414309070000015
wherein, L represents the information which is transmitted from right to left in the two types of information in the decoding process, namely left information;
Figure FDA0002414309070000016
the upper label 0 in the index represents the 0 th iteration, the S on the left of the index represents the S state in the factor graph, and the j on the right represents the j bit node in the factor graph; ln is the logarithm of the base e; p (y)j|xj0) represents the jth bit node y at the receiving endjProbability of correctly judging as 0; p (y)j|xj1) denotes the jth bit node y at the receiving endjProbability of correctly judging as 1;
step 2.C, initializing the information values of the rest bit nodes in the factor graph to 0;
step three, setting a judgment threshold T of an information value for each bit nodei,jAnd a maximum iteration number Iter, which specifically includes the following sub-steps:
step 3, setting of a judgment threshold value of a bit node connected with an additive check node in the A factor graph is obtained based on the formula (3) recursion;
Figure DEST_PATH_FDA0001879790340000017
wherein, the number on the left side of the subscript represents the number of states in the factor graph, i represents the ith state, and i +1 represents the (i + 1) th state; the numbers to the right of the subscript indicate the number of bit nodes in the factor graph, i.e., j indicates the jth bit node, j +2iDenotes the j +2 thiA bit node;
the initial threshold value for iteration is the initialization information value set in the step two;
Figure FDA0002414309070000026
the function is defined as formula (4);
Figure FDA0002414309070000022
step 3, setting the judgment threshold value of the bit node connected with the direct connection check node in the B factor graph is obtained by recursion based on the formula (5);
Figure FDA0002414309070000023
wherein, the number on the left side of the subscript represents the number of states in the factor graph, i represents the ith state, and i +1 represents the (i + 1) th state; the numbers to the right of the subscript indicate the number of bit nodes in the factor graph, i.e., j indicates the jth bit node, j +2iDenotes the j +2 thiA bit node;
step four, information values are transmitted to the left from the rightmost end bit node, and the method specifically comprises the following steps:
in the process of transmission, the information value of each current bit node is compared with a threshold value T set for each nodei,jComparing, if the threshold value is exceeded, transmitting the information value according to the formula (6), otherwise, updating leftwards according to the formula (7) and transmitting the information value of each bit node;
Figure FDA0002414309070000024
Figure FDA0002414309070000025
wherein i represents the ith state in the factor graph, j represents the jth bit node in the factor graph, t represents the tth iteration, and g (x, y) is 2tanh-1(tanh (x/2) tanh (y/2)) can be obtained byThe over-min-sum algorithm reduces the calculation to:
g(x,y)≈0.9sign(x)sign(y)min(|x|,|y|)；
step five, transferring an information value from the leftmost bit node to the right, specifically:
the information value of each current bit node is compared with a threshold value T set for each nodei,jComparing, and if the comparison result exceeds the threshold value, transmitting the information value according to the formula (6); otherwise, updating and transmitting the information value of each bit node to the right according to the formula (8);
Figure FDA0002414309070000031
step six, information values are transmitted to the left from the rightmost end bit node, and the method specifically comprises the following steps:
the information value of each current bit node is compared with a threshold value T set for each nodei,jComparing, if the comparison result exceeds the threshold value, transmitting the information value according to the formula (6), otherwise, updating leftwards according to the formula (7) and transmitting the information value of each bit node;
step seven, the appointed information value is transmitted from the leftmost end to the rightmost end and then transmitted from the rightmost end to the leftmost end, and an iteration process is performed, namely, each time an iteration is completed, the iteration is performed once corresponding to the step five and the step six; performing decoding judgment on each leftmost bit node every time iteration is performed according to the formula (9);
Figure FDA0002414309070000032
Figure FDA0002414309070000033
representing the decoding result of the jth bit node in the factor graph;
Figure FDA0002414309070000034
iter in (1) represents the maximum number of iterations;
step eight, judging whether the current iteration number reaches the maximum iteration number Iter, if so, jumping to the step ten, otherwise, jumping to the step nine;
step nine, performing CRC check on the decoding result, if the decoding result passes the CRC check, terminating the iteration process, and jumping to the step ten; otherwise, jumping to the step five, and continuing to perform the next iteration process;
step ten, outputting a decoding result.
2. The method of claim 1, wherein the method comprises: in step three, the threshold value T is determinedi,jIs based on a gaussian approximation algorithm.
3. The method of claim 1, wherein the method comprises: in the first step, the CRC check adopts 24-bit check.
4. The method of claim 1, wherein the method comprises: and the information value of each bit node is transmitted back and forth according to the fifth step and the sixth step, namely the decoding process is that the information value of each bit node is continuously transmitted back and forth between adjacent states in the factor graph, namely the process of the fifth step and the sixth step is continuously repeated.
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